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Chapter 19: Problem 69

Consider the following reaction between oxides of nitrogen: $$ \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g) $$ (a) Use data in Appendix \(C\) to predict how \(\Delta G\) for the reaction varies with increasing temperature. (b) Calculate \(\Delta G\) at \(800 \mathrm{~K}\), assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not change with temperature. Under standard conditions is the reaction spontaneous at $800 \mathrm{~K} ?\( (c) Calculate \)\Delta G\( at \)1000 \mathrm{~K}$. Is the reaction spontaneous under standard conditions at this temperature?

Short Answer

Expert verified
(a) The Gibbs Free Energy equation is given by \(\Delta G = \Delta H - T \Delta S\). (b) At 800 K, we have \(\Delta H = 55.8 \: kJ\), \(\Delta S = 173.5 \: J/K\), and \(\Delta G = -84,000 \: J/mol\). The reaction is spontaneous at 800 K, as \(\Delta G\) is negative. (c) At 1000 K, \(\Delta G = -117,700 \: J/mol\), which means the reaction is also spontaneous under standard conditions at 1000 K.

Step by step solution

01

a) Knowing the Gibbs Free Energy Equation:

We need to know the Gibbs Free Energy equation which is as follows: \[ \Delta G = \Delta H - T \Delta S \] where ∆G is the change in Gibbs free energy, ∆H is the change in enthalpy, T is the temperature in Kelvin, and ∆S is the change in entropy.
02

b) Calculating ∆G at 800 K:

We are given that ∆H° and ∆S° do not change with temperature. Using the data given in Appendix C, we have: ∆H°(NO2) = 33.1 kJ/mol, ∆S°(NO2) = 240.0 J/mol·K ∆H°(N2O) = 82.0 kJ/mol, ∆S°(N2O) = 218.6 J/mol·K ∆H°(NO) = 90.3 kJ/mol, ∆S°(NO) = 210.7 J/mol·K Now, we have to calculate the ∆H and ∆S of the reaction by using stoichiometric coefficients. ∆H = [3∆H°(NO)] - [∆H°(NO2) + ∆H°(N2O)] = (3*90.3) - (33.1+82.0) = 55.8 kJ ∆S = [3∆S°(NO)] - [∆S°(NO2) + ∆S°(N2O)] = (3*210.7) - (240.0+218.6) = 173.5 J/K Now we can calculate ∆G at 800 K: ∆G = ∆H - T∆S = 55.8*10^3 J/mol - (800 K)(173.5 J/mol·K) = -84,000 J/mol As ∆G is negative, the reaction is spontaneous at 800 K.
03

c) Calculating ∆G at 1000 K:

We already have ∆H and ∆S for the reaction; we only need to change the temperature in the equation for Gibbs Free Energy. ∆G = ∆H - T∆S = 55.8*10^3 J/mol - (1000 K)(173.5 J/mol·K) = -117,700 J/mol As ∆G is negative at 1000 K, the reaction is spontaneous under standard conditions at this temperature as well.

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Most popular questions from this chapter

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which 3 mol of gaseous reactants are converted to 2 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

Which of the following processes are spontaneous: (a) the evaporation of water at \(\$ T P\) to form water vapor of 101.3 kPa pressure; (b) separation of a mixture of water and oil into two separate phases; (c) the souring of milk; (d) the neutralization of hydrochloric acid with sodium hydroxide at \(\mathrm{STP} ;(\mathbf{e})\) the formation of ice from water at \(20^{\circ} \mathrm{C}\) and \(101.3 \mathrm{kPa} ?\)

Indicate whether each of the following statements is trueor false. If it is false, correct it. (a) The feasibility of manufacturing \(\mathrm{NH}_{3}\) from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\) depends entirely on the value of $\Delta H\( for the process \)\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) .$ (b) The reaction of \(\mathrm{Na}(s)\) with \(\mathrm{Cl}_{2}(g)\) to form \(\mathrm{NaCl}(s)\) is a spontaneous process. (c) A spontaneous process can in principle be conducted reversibly. (d) Spontaneous processes in general require that work be done to force them to proceed. (e) Spontaneous processes are those that are exothermic and that lead to a higher degree of order in the system.

Using data from Appendix \(\mathrm{C}\), write the equilibrium-constant expression and calculate the value of the equilibrium constant and the free- energy change for these reactions at \(298 \mathrm{~K}:\) (a) $\mathrm{NaHCO}_{3}(s) \rightleftharpoons \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g)$ (b) $2 \mathrm{HBr}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)+\mathrm{Br}_{2}(g)$ (c) $2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)$

Using data from Appendix \(\mathrm{C}\), calculate \(\Delta G^{\circ}\) for the following reactions. Indicate whether each reaction is spontaneous at $298 \mathrm{~K}$ under standard conditions. (a) \(2 \mathrm{Zn}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{ZnO}(s)\) (b) \(2 \mathrm{NaBr}(s) \longrightarrow 2 \mathrm{Na}(g)+\mathrm{Br}_{2}(g)\) (c) $\mathrm{CH}_{3} \mathrm{OH}(g)+\mathrm{CH}_{4}(g) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(g)+\mathrm{H}_{2}(g)$
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